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Solving London's Transport Problem

A new mathematical contest has just been announced by mathematical problem solving company eBourbaki. eBourbaki's mission is to solve the world's mathematical problems using contests to inspire innovation and creativity. They seek to help companies and organisations become more effective by facilitating creative mathematical solutions to
optimisation problems by:

improving mathematics engagement and education by working with teachers and professors to integrate eBourbaki contests into academic curricula,

and collaborating with clients to formulate soluble problems and then to interpret the solutions that grow out of contests for implementation.

The new contest is entitled Bicycles in London. London faces serious transportation challenges. With congestion charges on the rise and increased awareness of the environmental impact of many forms of commuting, cities are turning to bicycle stations to ease traffic, reduce pollution, improve parking, and enhance a green-friendly image. Last summer, Paris joined the ranks, instituting a
city-wide network of high-tech low-cost rental bicycle stations. The contest asks the question: if London were to embrace this concept, how would it best go about doing so? Where should the bike stations go? How many bikes at each station?

The contest will run May 5-12 2008 and full contest details, including a detailed problem statement, will be available on the website at the start of the contest. Winning solutions will be presented to the Mayor of London with the hope that students' recommendations will guide the way to helping London become a more liveable environment. The winning team will receive a prize of £1000.

The competition is open to UK students only, and students of mathematics, computer science and engineering are encouraged to enter. Participation requires contestants to register with the eBourbaki. Stay tuned to the website for contest rules and guidelines.

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A mathematician from the University of East Anglia has turned his gaze to the stars to try and answer one of humankind's oldest questions — are we alone in the Universe? And the unfortunate answer is, well, probably.

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Edward Lorenz, American mathematician and meteorologist, died in his Cambridge Massachusetts home on April 16 aged 90. Lorenz was the "father of chaos theory" and discovered the Lorenz attractor that often occurs in chaotic systems.

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The Enigma machine was once considered unbreakable, and the cracking of the "unbreakable code" by the allies changed the course of World War 2. Plus talks to Nadia Baker from the Enigma Project about the history of codes and code-breaking, why the Enigma machine was considered unbreakable, the mathematics behind codes, and how it was finally
cracked. The Enigma Project travels all over the United Kingdom and abroad, visiting over 100 schools and organisations, reaching over 12,000 people of all ages every year.

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Sixty-three year-old Avraham Trakhtman has solved one of the current generation's toughest mathematical problems — the 38 year-old road colouring problem. The solution will shortly be published in the Israel Journal of Mathematics.

Attacks on the foundations of calculus

George Berkeley was an Irish bishop and philosopher who is best known for his attacks on the logical foundations of the calculus as developed by Newton.

George Berkeley.

Berkeley started at Trinity College, Dublin at the tender age of 14 and graduated with a masters when only 18 years old. His attacks on the foundations of calculus were first aired in 1734 when he published The analyst: A discourse addressed to an infidel mathematician. The infidel mathematician is believed to have been either Edmond Halley or Isaac
Newton. He argued that although the calculus led to true results, its foundations were no more secure than those that underpin religion. He stated that the calculus involved a logical fallacy and described derivatives thus:

"And what are these fluxions? The velocities of evanescent increments? And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?"

In modern language, this could be read as:

"What are these 'instantaneous' rates of change? The ratios of vanishing increments? And what are these 'vanishing' increments? They are neither finite quantities nor 'infinitesimal' quantities, nor yet nothing. May we not call them the ghosts of departed quantities?"

His interesting theory as to why the calculus actually worked was that it was the result of two compensating errors.

As a consequence of the controversy surround Berkeley's publication, the foundations of calculus were rewritten in a much more formal and rigorous manner using limits. It was not until 1966, with the publication of Abraham Robinson's book Non-standard Analysis, that the concept of the infinitesimal was made rigorous. This gave an alternative way of
overcoming the difficulties that Berkeley found in Newton's approach.

Berkeley's influence in mathematics is reflected by the fact that the University of California, Berkeley, and the city of Berkeley that grew up around it, are named after him. Berkeley died of a heart attack on 14 January 1753, sitting with his family listening to his wife reading. He died so peacefully that the event went unnoticed, his family thinking he had fallen asleep. He left
instructions that he was not to be buried for at least five days and was buried at Christ Church, Oxford on 20 January.